It may be common practice, but rinsing your mouth out after brushing your teeth isn't a good idea. Redditor giubaloo explains why:

I know this this is not common practice, but it is actually quite important! Fluoride, one of the active ingredients in toothpaste, doesn't spend much time in contact when your teeth when you are brushing. Thus, it is crucial to let it work after you have already brushed your teeth. According to dentist Dr. Phil Stemmer, from The Fresh Breath Centre in London, "Rinsing washes away the protective flouride coating left by the toothpaste, which would otherwise add hours of protection." If you are thirsty drink a glass of water before brushing your teeth!

This is a pretty common tip from dentists. I've heard it from mine, and a quick Google search will turn up tons of recommendations saying the same thing. An article from The Guardian goes into more depth as well. This isn't a great idea for children who have yet to get their adult teeth in. Adults, however, will do just fine with a little leftover—just no mouthfuls of toothpaste, of course. For those who don't want to rinse their mouths out, however, they can pick up a fluoride rinse and just use that afterwards instead of water.